Synchronization of multiple chaotic FitzHugh-Nagumo neurons with gap junctions under external electrical stimulation

Authors:
Muhammad Rehan;Keum-Shik Hong;Muhammad Aqil
Affiliations:
Department of Cogno-Mechatronics Engineering, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea;Department of Cogno-Mechatronics Engineering, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea and School of Mechanical Engineering, Pusan National Unive ...;Department of Cogno-Mechatronics Engineering, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea
Venue:
Neurocomputing
Year:
2011

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Original articles: Synchronization of coupled chaotic FitzHugh-Nagumo neurons via Lyapunov functions

Mathematics and Computers in Simulation

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Abstract

This paper discusses the synchronization of three coupled chaotic FitzHugh-Nagumo (FHN) neurons with different gap junctions under external electrical stimulation. A nonlinear control law that guarantees the asymptotic synchronization of coupled neurons (with reduced computations) is proposed. The developed control law incorporates the synchronization error between two slave neurons in addition to the conventionally considered synchronization errors between the master and the slave neurons, which make the proposed scheme computationally more efficient. Further, a novel L"2 gain reduction criterion has been developed for multi-input multi-output systems with non-zero initial conditions, and is applied to robust synchronization of FHN neurons under L"2 norm bounded disturbance and uncertainties. Furthermore, a robust adaptive nonlinear control law is developed, which is capable of handling variations in nonlinear part of synchronization error dynamics, without using any neural-network-based training-oriented adaptive scheme. The proposed control schemes ensure global synchronization with computational simplicity, easy way of design and implementation and avoiding extra measurements. The results obtained with the proposed control laws are verified through numerical simulations.